## Exploration 32.1: Representation of Plane Waves

Move the slider and observe the animation on the left-hand panel of your screen. The animation shows the electric field in a region of space. The arrows show the field-vector representation of the electric field. The amplitude of the field is represented by the brightness of the arrows. The slider allows you to move along the z axis. Notice that the electric field is always uniform in the xy plane but varies along the z axis (position is given in meters and time is given in nanoseconds). Restart.

1. Construct a graph that represents the electric field along the z axis at t = 0 ns.

Now view a representation of the electric field. Click-drag inside the animation on the right to view the electric-field representation from different points of view. This representation should closely match the graph you drew for (a). Click on "play" to see a traveling wave. The representation on the right is often used to show a field like that on the left. Remember that the representation on the right is actually a graph of amplitude along the direction of propagation (z axis).

1. Keeping that in mind and looking at the graph on the right, rank the amplitude of the field at t = 0 ns for the following locations, from smallest to largest.
 Location x coordinate y coordinate z coordinate I 1 0 -1.5 II 1 1 -1.5 III 0 0 -1.5 IV 0 1 -1.0 V 1 1 -0.5
1. Now, push "play" to see the traveling wave. At position z = -0.5 m, rank the amplitude of the field at the following times (approximately), from smallest to largest.
 Time (ns) x coordinate y coordinate z coordinate t = 0 1 1 -0.5 t = 1.7 1 1 -0.5 t = 3.3 1 1 -0.5 t = 5.0 1 1 -0.5 t = 6.7 1 1 -0.5
1. What is the wavelength (distance between peaks) of the wave?
2. What is the frequency of the wave (the period T = 1/f is the time it takes for the wave to repeat itself at a given location)?
3. What is the speed of the wave? Exploration authored by Melissa Dancy and modified by Anne J. Cox.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

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